A stochastic preconditioned Douglas-Rachford splitting method for saddle-point problems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909329595039744 |
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| author | Dong, Yakun Bredies, Kristian Sun, Hongpeng |
| author_facet | Dong, Yakun Bredies, Kristian Sun, Hongpeng |
| contents | In this article, we propose and study a stochastic and relaxed preconditioned Douglas--Rachford splitting method to solve saddle-point problems that have separable dual variables. We prove the almost sure convergence of the iteration sequences in Hilbert spaces for a class of convex-concave and nonsmooth saddle-point problems. We also provide the sublinear convergence rate for the ergodic sequence concerning the expectation of the restricted primal-dual gap functions. Numerical experiments show the high efficiency of the proposed stochastic and relaxed preconditioned Douglas--Rachford splitting methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_13001 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A stochastic preconditioned Douglas-Rachford splitting method for saddle-point problems Dong, Yakun Bredies, Kristian Sun, Hongpeng Optimization and Control Numerical Analysis In this article, we propose and study a stochastic and relaxed preconditioned Douglas--Rachford splitting method to solve saddle-point problems that have separable dual variables. We prove the almost sure convergence of the iteration sequences in Hilbert spaces for a class of convex-concave and nonsmooth saddle-point problems. We also provide the sublinear convergence rate for the ergodic sequence concerning the expectation of the restricted primal-dual gap functions. Numerical experiments show the high efficiency of the proposed stochastic and relaxed preconditioned Douglas--Rachford splitting methods. |
| title | A stochastic preconditioned Douglas-Rachford splitting method for saddle-point problems |
| topic | Optimization and Control Numerical Analysis |
| url | https://arxiv.org/abs/2212.13001 |